The Full Maxwell

James Clerk Maxwell, as an object of scholarly study, is rather like the elephant that was characterized as a rope by one blind philosopher, as a wall by another and as a tree by a third: Maxwell made profound and crucial innovations to electromagnetic theory, including the electromagnetic theory of light; to the kinetic theory of gases and statistical mechanics; and to a variety of other areas—including color theory, the theory of Saturn's rings, vector analysis and control theory. It is thus understandable that Maxwell studies have suffered from a degree of Balkanization, with different groups of scholars concentrating on different aspects of Maxwell's work and hence seeing him differently. There have been attempts to see Maxwell whole, but these have been, for the most part, quite superficial, which is not surprising in view of various strains in the history-of-science discipline that militate for simplification and trivialization: the search for "paradigms" and the like, as simple, universal keys to the understanding of the scientific thought of the past; the attempt to "demystify" science by trivializing the great scientists of the past; and the need to simplify the relevant scientific ideas to accommodate an audience of general historians.

This book, in contrast, aims to take on the whole of Maxwell's thought, in a way that acknowledges its complexity, depth and nuance. Harman brings to this effort a rich familiarity with Maxwell's writings and their 19th-century context, honed through Harman's continuing work on an edition of Maxwell's scientific papers and letters, in three volumes, of which two have appeared to date. The result is a book on Maxwell's natural philosophy—on his scientific work, his views on the philosophy of science and his thoughts concerning science in relation to other areas of thought and concern—which, making use of both the primary sources that Harman knows so well and the relevant secondary sources, marks an important stage in the maturation of Maxwell studies and the synthesis of a broad account of Maxwell's scientific views and accomplishments. The book is wonderfully informative and insightful throughout; its merit lies as much in stimulating questions as in providing answers.

Characteristic is Harman's treatment of the methodological parallels and relations between Maxwell's work in electromagnetic theory and his work in gas theory—a topic of the utmost importance for understanding the coherence of Maxwell's work. Harman artfully renders the nuances in Maxwell's use of mechanical models in electromagnetic theory: Maxwell began in an agnostic vein, using the method of physical analogy; he drew a parallel between electromagnetic field lines and the flow lines of an incompressible fluid through a resisting medium, without any suggestion that such a fluid was flowing in an actual electric or magnetic field. In his next major paper, he moved on to a realistically intended mechanical theory of electromagnetic phenomena, in which an elastic cellular medium—a mechanical ether—was taken to be the actual basis of electromagnetic phenomena. In his ultimate statement of electromagnetic theory, he retreated from the concrete mechanical model to a much more abstract, Langrangian formulation of field theory. The question then is, how does this progression of thought with respect to mechanical models in electromagnetic theory relate to Maxwell’s work in gas theory?

Maxwell's first major paper in gas theory, "Illustrations of the Dynamical Theory of Gases," turns out to have some of the characteristics of Maxwell's first approach to electromagnetic theory—in which a physical analogy was proposed, without realistic intent—but also some of the characteristics of his subsequent effort in electromagnetic theory, in which a mechanical theory was proposed, with serious realistic intent. Building on Harman's analysis, which emphasizes the realistic intent of Maxwell’s first paper on gas theory, I think the account can be enriched by drawing parallels with William Thomson's use of mechanical models and by giving attention to the issue of linear as against rotational motions in the conceptualization of thermal phenomena. Harman’s treatment of Maxwell's approach to mechanical modeling, as cutting across gas theory and electromagnetic theory, thus both provides important insights and opens vistas for further research concerning Maxwell's evolving stance with respect to the mechanical worldview.

But this is to pick out just a small piece of Harman's account; what is most impressive about this book is its treatment of the whole range of Maxwell's activity as a natural philosopher with this kind of depth and nuance, making possible a synthesis that constitutes authentic progress in Maxwell studies. The more one understands of Maxwell, the more one's admiration of him grows.—Daniel M. Siegel, History of Science, University of Wisconsin, Madison